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In this paper we study the distribution of the non-trivial zeros of theRiemann zeta-function $\zeta(s)$ (and other L-functions) using Montgomery'spair correlation approach. We use semidefinite programming to improve uponnumerous asymptotic bounds in the theory of $\zeta(s)$, including theproportion of distinct zeros, counts of small gaps between zeros, and sumsinvolving multiplicities of zeros.

Pair Correlation Estimates for the Zeros of the Zeta Function via Semidefinite Programming